Parameters, such as a temperature of a component in a gas turbine aircraft engine, are commonly measured and indicated by signals which are not completely accurate, but exhibit statistical properties, such as noise. The invention concerns setting alarm points for such measured parameters.
FIG. 1 is a schematic of a measurement system, which measures an actual parameter 3. Actual parameter 3 can, in general, be any parameter of interest, such as a temperature, dimension, acceleration, velocity, and so on. Measurement apparatus 6 produces a signal, called the measurement signal 9, which is intended to indicate the value of the actual parameter 3.
However, in many instances, the measurement signal 9 does not exactly correspond to the actual parameter 3 itself. This can occur, for example, if (1) the measurement signal 9 takes the form of an electrical voltage, and (2) the voltage is small, say in the range of millivolts. In such a case, electrical noise, due to the random thermal motion of electrons, is also present in the form of a fluctuating voltage. The measurement signal 9 will contain both (1) the voltage indicating the actual parameter 3 and also (2) the electrical noise.
Because of the noise present and other reasons, many times the measurement signal 9 will behave as a random variable. The random properties create problems when one attempts to use the measurement signal 9 to infer whether the actual parameter 3 has exceeded a limit.
A simplified example will illustrate the problem. Assume that, as in FIG. 2, the actual parameter 3 is constant. If the measurement process has Gaussian properties, then the measurement signals 9 which will be obtained will be scattered about the actual parameter 3. Circles 9 indicate generically the scattered measurement signals 9. FIG. 6, discussed later, illustrates one type of scatter in greater detail. The measurement signals 9 in FIG. 2 have a mean M and a standard deviation S.
Because of the characteristics of a Gaussian distribution, 68.2 percent of the time, the measurement signal 9 will lie between (M+S) and (Mxe2x88x92S), that is, within one standard deviation S from the mean M. (68.2=34.1+34.1.)
The measurement signal 9 will lie between (M+S) and (M+2S) 13.6 percent of the time, and so on, as indicated for the other deviations from M.
Assume a limit 15 to exist, called an alert limit or alarm limit, which the actual parameter 3 of FIG. 1 should not exceed. Limit 15 may represent a specific speed or temperature. Clearly, a problem arises in inferring whether that limit 15 has been exceeded, based on the measurement signal 9. Even if the underlying parameter 3 is constant, as indicated, nevertheless the random properties of the measurement signal 9 can cause it to exceed limit 15. For example, measurement signal 9A exceeds the limit 15, even though the actual parameter 3 is constant, and below the limit 15.
Therefore, statistical properties of measurement signals can give false indications that a limit has been exceeded, even if all measuring equipment is operating properly.
In one form of the invention, a measurement signal is derived from a physical parameter and is compared with a limit, to infer whether the physical parameter has reached an undesirable value. If so, an alarm signal is issued. The invention sets the limit by (1) synthesizing numerous instances of the measurement signal, (2) comparing them against different limits to produce alarm signals, and (3) selecting the limit which produces alarm signals having a desired accuracy, or probability of being correct. That limit is used in practice.